Alcón, Liliana Bonomo, Flavia Durán, Guillermo Gutierrez, Marisa Mazzoleni, María Pía Ries, Bernard Valencia-Pabon, Mario 2018 Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex of the graph a nontrivial path on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. For a nonnegative integer k, Bk-EPG graphs are defined as EPG graphs admitting a model in which each path has at most k bends. Circular-arc graphs are intersection graphs of open arcs of a circle. It is easy to see that every circular-arc graph is a B4-EPG graph, by embedding the circle into a rectangle of the grid. In this paper, we prove that circular-arc graphs are B3-EPG, and that there exist circular-arc graphs which are not B2-EPG. If we restrict ourselves to rectangular representations (i.e., the union of the paths used in the model is contained in the boundary of a rectangle of the grid), we obtain EPR (edge intersection of paths in a rectangle) representations. We may define Bk-EPR graphs, k ≥ 0, the same way as Bk- EPG graphs. Circular-arc graphs are clearly B4-EPR graphs and we will show that there exist circular-arc graphs that are not B3-EPR graphs. We also show that normal circulararc graphs are B2-EPR graphs and that there exist normal circular-arc graphs that are not B1-EPR graphs. Finally, we characterize B1-EPR graphs by a family of minimal forbidden induced subgraphs, and show that they form a subclass of normal Helly circular-arc graphs. application/pdf https://folia.unifr.ch/global/documents/307803 https://folia.unifr.ch/documents/307803/files/epg2_rero.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2016.08.004 info:eu-repo/semantics/openAccess License undefined Discrete applied mathematics. - 2018, vol. 234, p. 12-21 Edge intersection graphs paths on a grid forbidden induced subgraphs (normal, Helly) circular-arc graphs powers of cycles info:eu-repo/classification/udc/33 On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid http://purl.org/coar/resource_type/c_6501